bro keep going, I really really love maths but now I don't do it anymore because of job and stuffs, everytime you post a question I take it as a riddle and try to solve it its fun, maths used to be my escape in my school days, these questions really give me that feeling back
Great problem and great solution! Quick tip - when you reference a formula, on the side, substitute the expressions from the problem into the variables of the formula to make it clearer. I hope this channel grows!
TWO real solutions from x^2= sqrt(8) so x=+ - sqrt of sqrt(8) so x = + - Fourth Root (8) = + - (8)^(1/4). If we search for complex solutions the other two are from x^2 = sqrt( - 8) so x = + - sqrt (sqrt (8*i^2))= + - ( Fourth Root 8 ) * i = + - ( i * 8^(1/4) ) . NOTE : Equation x^4 = 16 = 2^4 has TWO real solutions + - 2 = + - Fourth Root(16)
But doesn't x^4 = 8 have four roots? We get x² = ±√8 = ±2√2, and that gives us two quadratics to solve, x²±2√2=0 , yielding x=±√(±2√2)/2, which are the four roots.
Sorry, I'm not a professional researcher nor math teacher, so I don't know the correct answer. If it is surely just a problem of x⁴=8, it is true that four roots can be found, but since this is a power part of the exponent, it is doubtful whether it can be considered in the same way as a normal calculation. The study of large numbers is about making exponents into multiple nested structures and how to devise ways to make them larger with simple expressions. If the expression of this problem is also included in the category of large numbers, it seems to be a rule to exclude imaginary numbers. Therefore, unfortunately, I don't think anyone can say the correct answer unless they know the details.
@@poppylikecats -- Why aren't we considering complex roots? You just made that up. If you are taking a math test and you have a question like what are the possible values of x in x^4=16, there are four solutions and you should present all four or you'll lose points. What are the four solutions?
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Fantastic.
Keep going! 👍
bro keep going, I really really love maths but now I don't do it anymore because of job and stuffs, everytime you post a question I take it as a riddle and try to solve it its fun, maths used to be my escape in my school days, these questions really give me that feeling back
Oh wow, I'm very glad to see this! Thank you for support, I really appreciate it!
Great problem and great solution! Quick tip - when you reference a formula, on the side, substitute the expressions from the problem into the variables of the formula to make it clearer. I hope this channel grows!
✍️
TWO real solutions from x^2= sqrt(8) so x=+ - sqrt of sqrt(8) so x = + - Fourth Root (8) = + - (8)^(1/4).
If we search for complex solutions the other two are from x^2 = sqrt( - 8) so x = + - sqrt (sqrt (8*i^2))=
+ - ( Fourth Root 8 ) * i = + - ( i * 8^(1/4) ) .
NOTE : Equation x^4 = 16 = 2^4 has TWO real solutions + - 2 = + - Fourth Root(16)
But doesn't x^4 = 8 have four roots? We get x² = ±√8 = ±2√2, and that gives us two quadratics to solve, x²±2√2=0 , yielding x=±√(±2√2)/2, which are the four roots.
Sorry, I'm not a professional researcher nor math teacher, so I don't know the correct answer. If it is surely just a problem of x⁴=8, it is true that four roots can be found, but since this is a power part of the exponent, it is doubtful whether it can be considered in the same way as a normal calculation. The study of large numbers is about making exponents into multiple nested structures and how to devise ways to make them larger with simple expressions. If the expression of this problem is also included in the category of large numbers, it seems to be a rule to exclude imaginary numbers. Therefore, unfortunately, I don't think anyone can say the correct answer unless they know the details.
x=±√(±2√2)/2 is 2 roots not 4, it does have 4 roots if you consider complex roots however (which we aren't).
@@poppylikecats -- Why aren't we considering complex roots? You just made that up. If you are taking a math test and you have a question like what are the possible values of x in x^4=16, there are four solutions and you should present all four or you'll lose points. What are the four solutions?
@@佐藤広-q2u -- The study of large numbers? Where is all this coming from?
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